Related Concepts: 5.04 Wave Polarization & Ionospheric Sky-Wave Radio Propagation | 5.05 Dispersion, Phase & Group Velocity, Doppler Effect & Brewster’s Angle | 5.07 Solved PYQ Numerical Bank - Waves & Propagation

5.06 Radio Wave Propagation Modes & Ionospheric Effects

Study Checklist & Core Objectives

• Classify the Three Propagation Modes: Master frequency ranges, mechanisms, typical ranges, and practical applications of Ground, Sky, and Space waves. [PYQ: 2017, 2018, 2023]
• Determine Service Mode Selection: Explain the physical and engineering reasons why SW, FM, Cellular, and Satellite services use their respective modes. [PYQ: 2015, 2019, 2021, 2022]
• Derive Line-of-Sight (LOS) Link Geometry: Mathematically derive the maximum line-of-sight distance formula over a curved Earth, including the tropospheric $4/3$ refractive index correction. [PYQ: 2016, 2019]
• Analyze Ground Wave Frequency Limits: Explain why ground wave propagation becomes highly unsuitable for frequencies exceeding $2\text{ MHz}$ using conduction losses and soil skin depth relationships. [PYQ: 2016]
• Assess Earth Curvature Effects: Evaluate the impact of Earth’s curvature on wave propagation, including radio horizons, low-frequency diffraction, shadow zones, and tropospheric refraction. [PYQ: 2016]
• Formulate TEM Wave Characteristics: Construct a short note defining Transverse Electromagnetic (TEM) wave criteria and cross-product propagation vector relations.

---

🗺️ Radio Wave Propagation Classification Tree

graph TD
    A[Radio Wave Propagation] --> B[Ground Wave / Surface Wave]
    A --> C[Sky Wave / Ionospheric Wave]
    A --> D[Space Wave / Tropospheric / LOS]

    B --> B1[Frequency: < 2 MHz]
    B --> B2["Mechanism: Diffracts along Earth's curvature"]

    C --> C1[Frequency: 3 - 30 MHz]
    C --> C2["Mechanism: Refraction in Ionospheric Layers"]

    D --> D1[Frequency: > 30 MHz]
    D --> D2["Mechanism: Line-of-Sight & Tropospheric Bending"]

---

1. The Three Fundamental Propagation Modes [PYQ: 2017, 2018, 2023]

Electromagnetic waves propagate from a transmitting antenna to a receiving antenna through three distinct physical mechanisms depending on the operating frequency, antenna design, and atmospheric interaction.

       [Space Wave (Line-of-Sight)]
       Transmitter --------------> Receiver
             \                      /
              \ [Sky Wave]         /
               \    /\            /  <-- Ionosphere (Reflects HF)
                \  /  \          /
                 \/    \        /
  Transmitter ----*-----\------*---- Receiver
  \\\\\                    /////     <-- Earth's Surface
       `---[Ground Wave]---`         (Guided along surface curvature)

A. Ground Wave (Surface Wave) Propagation

• Frequency Range: Very Low Frequency (VLF) to Medium Frequency (MF), typically below $2\text{ MHz}$.
• Physical Mechanism:
  • The wave travels along the boundary between the Earth’s surface and the atmosphere.
  • The wavefront is dynamically guided by the conductive Earth. As the wave travels, it induces charges on the ground’s surface, creating a current return path that tilts the wavefront forward. This tilt allows the wave to bend or diffract {bend around the physical obstacle of the curved horizon} around the Earth’s curvature.
• Typical Range: Up to thousands of kilometers at VLF; hundreds of kilometers at MF.
• Practical Examples:
  1. VLF Maritime Navigation: Used for global submarine communications due to the low attenuation {the gradual loss of signal strength or amplitude over distance} of ground waves over highly conductive seawater.
  2. AM Radio Broadcasting (535 kHz–1605 kHz): Local AM radio stations rely on ground waves to provide stable day-and-night coverage within a hundred-mile radius.

B. Sky Wave (Ionospheric) Propagation

• Frequency Range: High Frequency (HF), typically $3\text{ MHz}$ to $30\text{ MHz}$.
• Physical Mechanism:
  • EM waves radiated at oblique {slanted or non-perpendicular} angles toward the sky enter the ionized layers of the upper atmosphere (the ionosphere).
  • As the wave encounters increasing free electron density $N$, its refractive index drops (governed by the plasma permittivity equation detailed in [[5.04 Wave Polarization & Ionospheric Sky-Wave Radio Propagation]]).
  • The wave is gradually bent (refracted {curved away from its straight path due to changing density}) away from the normal until it undergoes total internal reflection, directing it back down to the Earth’s surface.
• Typical Range: Single-hop propagation ranges up to $4000\text{ km}$; global coverage is possible through multi-hop ground-ionosphere reflections.
• Practical Examples:
  1. International Shortwave Broadcasting: Services like BBC World Service or Voice of America utilize HF bands to broadcast news globally across continents.
  2. Amateur (HAM) Radio Communication: Operators establish long-distance point-to-point voice and data links over thousands of miles without infrastructure.

C. Space Wave (Tropospheric / Line-of-Sight) Propagation

• Frequency Range: Very High Frequency (VHF) and above, typically above $30\text{ MHz}$.
• Physical Mechanism:
  • At frequencies above $30\text{ MHz}$, the wave energy easily penetrates the ionosphere without being reflected (since the operating frequency $f$ is much greater than the peak plasma frequency $f_p$).
  • Propagation is thus restricted to the troposphere {the lowest part of Earth’s atmosphere where weather occurs, up to ~15 km} and must occur via direct Line-of-Sight (LOS) paths, ground-reflected waves, or tropospheric scatter {scattering of radio waves by air density fluctuations in the troposphere}.
• Typical Range: Strictly limited by the radio horizon (typically $50\text{–}80\text{ km}$ for terrestrial antennas).
• Practical Examples:
  1. Cellular Telephony (LTE/5G): High-bandwidth local links operating in UHF/microwave bands between towers and user terminals.
  2. Satellite Communications & GPS: Ground-to-space links operating in GHz bands that easily penetrate the atmospheric and ionospheric layers to reach orbiting satellites.

---

Comparison Matrix of Propagation Modes

Parameter	Ground Wave	Sky Wave	Space Wave
Frequency Band	VLF, LF, MF ($<2\text{ MHz}$)	HF ($3\text{ MHz}-30\text{ MHz}$)	VHF, UHF, SHF ($>30\text{ MHz}$)
Primary Mechanism	Diffraction along Earth’s surface	Ionospheric refraction (reflection)	Direct line-of-sight path
Typical Range	Up to $1000\text{s of km}$ (VLF)	Up to $4000\text{ km}$ per hop	Limited by radio horizon ($50\text{–}80\text{ km}$)
Atmospheric Layer	Ground-troposphere interface	Ionosphere ($50\text{–}500\text{ km}$ altitude)	Troposphere only ($<15\text{ km}$)
Bandwidth Capacity	Extremely low	Low to Moderate	High to Extremely High
Dominant Loss	Ground conduction losses & tilt	Ionospheric absorption	Atmospheric absorption & free-space path loss

---

2. Mode Selection per Service & Physical Rationale [PYQ: 2015, 2019, 2021, 2022]

A. Shortwave (SW) Radio Broadcasting

• Selected Mode: Sky Wave Propagation ($3\text{ MHz}-30\text{ MHz}$).
• Physical Reason:
  • The goal of Shortwave broadcasting is cost-effective, continental, or global coverage from a single high-power transmitter.
  • The HF band is perfectly suited because these frequencies are lower than the maximum usable frequency (MUF) of the ionosphere, allowing the wave to undergo total internal reflection.
  • This refraction allows the signals to bypass the curvature of the Earth over thousands of kilometers via ionospheric hops, avoiding the massive ground absorption that occurs at these frequencies.

B. FM Radio Broadcasting [PYQ: 2015]

• Selected Mode: Space Wave / Line-of-Sight Propagation ($88\text{ MHz}-108\text{ MHz}$ within VHF).
• Physical Reason:
  • FM broadcasting requires high fidelity, wide bandwidth ($200\text{ kHz}$ per channel), and a highly stable, noise-free signal.
  • At VHF ($>30\text{ MHz}$), ground waves suffer extreme attenuation, and sky waves completely penetrate the ionosphere, making ionospheric sky-wave propagation impossible.
  • Using Space Wave propagation provides a highly stable line-of-sight terrestrial path. Because the waves are not subject to fluctuating ionospheric conditions (which cause fading {the fluctuation in received signal strength over time} in AM shortwave), FM reception remains clean, highly predictable, and immune to ionospheric atmospheric noise.

C. Cellular Telephones

• Selected Mode: Space Wave Propagation (UHF/Microwave bands, typically $700\text{ MHz}-3.5\text{ GHz}$).
• Physical Reason:
  • Cellular systems operate on a frequency-reuse grid model where geographical zones are divided into small “cells.”
  • At UHF and microwave frequencies, the signals are limited to localized Line-of-Sight space wave propagation.
  • This rapid spatial attenuation and horizon limit are advantageous because they prevent interference between distant cells operating on the same frequency.
  • Furthermore, these high frequencies accommodate the wide channel bandwidths required for modern high-speed data transmission (which would be impossible in the narrow LF/MF/HF bands).

D. Satellite Communication

• Selected Mode: Space Wave / Direct Penetration (SHF/EHF bands, typically $1\text{ GHz}-30\text{ GHz}$).
• Physical Reason:
  • Satellite links require straight-line paths through the entire depth of the Earth’s atmosphere to reach orbiting spacecraft.
  • Operating at frequencies far above the ionospheric critical frequency ($f_c\approx 9\text{ MHz}$) ensures that the wave completely penetrates both the tropospheric refractive index gradients and the ionospheric plasma layers without being reflected or experiencing severe refraction.
  • Frequencies in the GHz range also minimize ionospheric scintillation {rapid fluctuation in amplitude and phase of a radio signal passing through the ionosphere} and permit the use of highly directional, high-gain parabolic dish antennas with small physical dimensions.

---

3. Line-of-Sight (LOS) Link Geometry [PYQ: 2016, 2019]

Because space waves travel in straight lines, terrestrial communication is limited by the geometric curvature of the Earth. Beyond a certain distance, the curved Earth acts as a physical barrier, creating a shadow zone.

                  Direct Line-of-Sight (d)
       Tx  o------------------------------------o  Rx
          /|                                    |\
         / | h_t                                | \ h_r
        /  |                                    |  \
       /   |                                    |   \
      /____|_____________ Horizon ______________|____\
     \     |              Tangent               |     /
      \    |                                    |    /
       \   |                                    |   /
        \  |                                    |  /
         \ |                                    | /
          \|                                    |/
           o                                    o
            \                                  /
             \               Earth            /
              \            Radius (R)        /
               \                            /
                \                          /
                 \                        /
                  \                      /
                   \                    /
                    \                  /
                     \                /
                      \              /
                       \            /
                        \  Angle   /
                         \   θ    /
                          \      /
                           \    /
                            \  /
                             \/
                             Origin

Derivation of the Maximum LOS Distance

Let:

• $R$ = True physical radius of the Earth ($\approx 6370\text{ km}$).
• $h_t$ = Physical height of the transmitting antenna above the surface [m].
• $h_r$ = Physical height of the receiving antenna above the surface [m].
• $d_t$ = Horizon distance of the transmitting antenna [km].
• $d_r$ = Horizon distance of the receiving antenna [km].
• $d$ = Maximum total Line-of-Sight communication distance [km] ($d=d_t+d_r$).

Applying the Pythagorean theorem to the right-angled triangle formed by the transmitter, the Earth’s center, and the tangent point on the horizon: $(R+h_t{)}^2=R^2+d_t^2$

Expanding both sides: $R^2+2R{h}_t+h_t^2=R^2+d_t^2$ $2R{h}_t+h_t^2=d_t^2$

Since the antenna height is negligible compared to the Earth’s radius ($h_t\ll R$), the term $h_t^2$ is extremely small and can be safely neglected: $d_t^2\approx 2R{h}_t⟹d_t=\sqrt{2R{h}_t}$

Similarly, for the receiver antenna horizon distance: $d_r\approx \sqrt{2R{h}_r}$

The maximum total line-of-sight communication distance $d$ is the sum of the transmitting and receiving horizon distances: $d=d_t+d_r=\sqrt{2R{h}_t}+\sqrt{2R{h}_r}$

---

Conversion to Practical Units (Terrestrial Metric Form)

Using the physical radius of the Earth, $R\approx 6370\text{ km}=6.37\times 10^6\text{ m}$:

For $d_t$ in kilometers and $h_t$ in meters: $d_t(\text{km})=\frac{\sqrt{2\times (6.37\times 10^6\text{ m})\times h_t(\text{m})}}{1000}$ $d_t(\text{km})=\frac{\sqrt{12.74\times 10^6}\times \sqrt{h_t}}{1000}=\frac{3570\times \sqrt{h_t}}{1000}\approx 3.57\sqrt{h_t}$

Summing the transmitter and receiver components yields the optical line-of-sight distance: $d(\text{km})\approx 3.57\left(\sqrt{h_t}+\sqrt{h_r}\right)$

---

The $4/3$ Effective Earth Radius Refraction Variant

In the physical troposphere, the air density (and thus the refractive index $n$) decreases with height. This continuous refractive index gradient causes electromagnetic waves to bend slightly downward toward the Earth, allowing them to propagate slightly beyond the geometric optical horizon.

To account for this tropospheric bending without using complex refraction math, engineers use the effective Earth radius concept (originated by shell slides/Kennedy): $R^{\prime }=kR=\frac{4}{3}R$

Replacing $R$ with $R^{\prime }\approx 1.33\times 6370\text{ km}\approx 8493\text{ km}$ in the metric conversion: $d_t(\text{km})=\frac{\sqrt{2\times (8.493\times 10^6\text{ m})\times h_t(\text{m})}}{1000}\approx 4.12\sqrt{h_t}$

Thus, the radio line-of-sight distance (the official standard used in this course) is: $d(\text{km})\approx 4.12\left(\sqrt{h_t}+\sqrt{h_r}\right)$

Exam Tip: Optical vs. Radio Horizon

For exams, explicitly state whether you are calculating the geometric optical horizon ($k=1⟹3.57$) or the practical radio horizon ($k=4/3⟹4.12$). The course slides and Kennedy textbook default to the $4.12$ radio refraction standard.

---

4. Why Ground Waves Fail Above 2 MHz [PYQ: 2016]

Ground wave propagation is highly efficient at low frequencies but becomes completely unusable for frequencies exceeding approximately $2\text{ MHz}$ due to two physical loss mechanisms:

A. Conduction Losses Scale Directly with Frequency

As a surface wave propagates, it sweeps across the ground, inducing alternating electric currents in the soil. Because the Earth is a lossy dielectric conductor with finite conductivity ($\sigma$), these induced currents encounter electrical resistance, dissipating wave energy as heat (Joule heating). The rate of this energy dissipation is proportional to the electric field’s frequency. As the frequency increases, the rate of charge displacement increases, leading to a rapid rise in power attenuation.

B. Skin Depth Relationship and Wave Absorption

The penetration depth of the induced currents into the Earth’s soil is governed by the skin depth ($\delta$) formula derived in [[5.02 Plane Waves in Lossless vs. Lossy Media & Skin Depth Calculations]]: $\delta =\frac{1}{\alpha }=\sqrt{\frac{2}{\omega \mu \sigma }}=\frac{1}{\sqrt{\pi f\mu \sigma }}$

This relation shows that skin depth is inversely proportional to the square root of frequency ($\delta \propto 1/\sqrt{f}$):

1. At Low Frequencies ($<2\text{ MHz}$): The skin depth $\delta$ is deep. The induced current spreads over a large volume of the Earth’s crust, keeping current density low and minimizing resistive power dissipation.
2. At High Frequencies ($>2\text{ MHz}$): The skin depth becomes extremely thin. The induced currents are confined to a very thin layer at the surface, drastically increasing current density and resistive $I^{2}R$ losses.

As a result, practically all the wave’s energy is absorbed by the ground within a short distance of the transmitter.

---

5. Earth Curvature Effects on Propagation [PYQ: 2016]

The spherical shape of the Earth imposes several critical physical constraints on EM waves traveling through the atmosphere:

                            Space Wave
                           Line-of-Sight
                      _..---''   |   ``---.._
           Tx _..---''           |           ``---.._ Rx
          .---'                  |                   `---.
         /                       |                        \
        |                        |                         |
        |      Diffraction       |       Shadow Zone       |
        |    (Low Frequency)     |     (High Frequency)    |
         \                       |                        /
          `---.                  |                   .---'
               ``---.._          |           _..---''
                       ``---.._  |   _..---''

A. The Radio Horizon

Due to the Earth’s curvature, direct straight-line space wave propagation is blocked once the path becomes tangent to the Earth’s surface. This limits terrestrial space-wave communications to a maximum distance governed by the transmitter and receiver antenna heights.

B. Diffraction at Low Frequencies

At low frequencies (VLF to LF), the wavelength of the signal is long compared to the obstacles on the Earth’s surface. According to Huygens’ Principle, the wavefront constantly diffracts around the curved profile of the Earth, allowing ground waves to follow the Earth’s surface far beyond the optical horizon.

C. Tropospheric Refraction (The $4/3$ Earth Radius)

As altitude increases, atmospheric density and temperature drop, causing the refractive index of air ($n$) to decrease. This vertical gradient ($dn/dh<0$) constantly bends space waves back toward the Earth. This refraction expands the effective communication horizon, which is modeled mathematically by scaling the Earth’s radius by $4/3$.

D. Shadow Zones

At VHF frequencies and above, the wavelengths are too short to diffract significantly around the Earth’s curvature. Consequently, the region beyond the radio line-of-sight tangent point becomes a physical shadow zone {areas where direct line-of-sight signals cannot reach due to obstruction by the Earth’s curvature} where the direct space-wave field strength drops to zero.

---

6. Key Ionospheric Parameters & Terms [PYQ: 2015, 2016, 2018, 2020, 2021]

In sky-wave propagation, the ionosphere behaves as a refracting medium. To design radio links, we define several critical parameters:

A. Critical Frequency ($f_c$) [PYQ: 2016, 2018]

• Definition: The highest frequency that is returned to Earth by an ionospheric layer when transmitted vertically upward.
• Physical Basis: A wave sent vertically will penetrate the layer and escape into space if its frequency $f>f_c$. It is given by: $f_c=\frac{1}{2\pi }\sqrt{\frac{N_{max}{e}^2}{m{ϵ}_0}}\approx 9\sqrt{N_{max}}$ where $N_{max}$ is the peak electron density of the layer [electrons/m³].

B. Virtual Height ($h^{\prime }$) [PYQ: 2015, 2016, 2018, 2020, 2021, 2022]

• Definition: The apparent height of an ionospheric layer, calculated by assuming the wave travels in a straight line at the speed of light $c$ for the entire round trip and undergoes sharp reflection at a single point: $h^{\prime }=\frac{ct}{2}$ where $t$ is the round-trip echo time measured by an ionosonde.

                  Virtual Height (h')
            Actual Height (h) _.-'--._
                           _.-'        '-._
            Tx -----------*----------------*----------- Rx
              \          /                  \         /
               \        /                    \       /
                \      /   Actual Path        \     /
                 \    /                        \   /
                  \  /                          \ /
    ===============\/============================\/============== Earth's Surface

Why Virtual Height is Used in Calculations Instead of Actual Height [PYQ: 2018, 2020, 2021]

1. Actual Height is Unmeasurable: The wave is gradually bent (refracted) over a thick ionized region rather than reflected from a sharp surface. Since there is no single physical boundary, the actual reflection height cannot be measured directly.
2. Refractive Slowdown: Within the ionized layer, the wave’s group velocity decreases below $c$. This delay causes the round-trip time $t$ to be longer, meaning the calculated virtual height $h^{\prime }$ is always greater than the actual physical peak height of the ray path ($h^{\prime }>h$).
3. Geometric Simplicity & Correctness: Geometrically, using the virtual height $h^{\prime }$ with straight-line rays forming a triangle yields the exact same ground range $D$ and antenna take-off angle as the actual curved refraction path. Thus, it simplifies link planning without introducing errors.

C. Skip Distance ($D_{skip}$) [PYQ: 2015, 2016, 2018]

• Definition: The minimum distance from a transmitting antenna at which a sky wave of a given frequency (above $f_c$) will return to Earth.
• The Skip Zone: Within the skip distance, the angle of incidence is too steep (closer to normal), causing the wave to penetrate the layer and escape. The region between the ground-wave coverage limit and the first sky-wave return point is a shadow zone known as the skip zone, where no signal is received.

D. Maximum Usable Frequency (MUF) [PYQ: 2015, 2016, 2018]

• Definition: The highest frequency that can be used for reliable communication between two specific points on Earth via ionospheric refraction.
• The Secant Law: $\text{MUF}=f_c\sec {\theta }_i=f_c\sqrt{1+{\left(\frac{D}{2h^{\prime }}\right)}^2}$ where ${\theta }_i$ is the angle of incidence at the virtual reflection point and $D$ is the ground distance. MUF is always greater than or equal to $f_c$.

E. Minimum Usable Frequency (LUF / MUF${}_{min}$) [PYQ: 2018]

• Definition: The lowest frequency that can establish a reliable sky-wave link. Below this frequency, the wave is heavily absorbed in the lower D-layer of the ionosphere due to collisions between free electrons and neutral molecules, converting wave energy to heat.

---

7. Transverse Electromagnetic (TEM) Waves

(Source: Sanglap Sir / Lecture 11-12 slides)

A Transverse Electromagnetic (TEM) Wave is a wave where both the Electric field ($\vec{E}$) and the Magnetic field ($\vec{H}$) are entirely transverse (perpendicular) to the direction of wave propagation.

       ^ Y (Electric Field vector E)
       |
       |     ___
       |    /   \         Direction of Propagation (vector k = E x H)
       |   /     \                      =======> (along Z-axis)
-------o---------------------------------------------------> Z
      / \       /
     /   \     /
    /     `---'
   /
  v X (Magnetic Field vector H)

Critical Mathematical Criteria of TEM Waves

1. No Axial Components: There are no electric or magnetic field components along the direction of propagation (assumed here to be the $z$-axis): $E_z=0,H_z=0$
2. Orthogonality: The electric and magnetic fields are always perpendicular to each other: $\vec{E}\cdot \vec{H}=0$
3. Poynting Vector & Propagation Direction: The direction of wave travel is given by the cross product of the electric and magnetic field vectors: $\vec{\mathcal{P}}=\vec{E}\times \vec{H}$ If $\vec{E}$ is oriented along ${\hat{a}}_x$ and $\vec{H}$ is oriented along ${\hat{a}}_y$, the wave propagates along the $+z$-direction: ${\hat{a}}_x\times {\hat{a}}_y={\hat{a}}_z$

---

8. Numerical Linkage (Cross-Reference)

The standard application problem matching this note’s Line-of-Sight derivation is the VHF LOS Link Budget and Field Strength Problem [PYQ: 2017]:

A VHF communication link is to be established with a $35\text{ W}$ transmitter at $90\text{ MHz}$. Find the maximum distance up to which line-of-sight communication is possible if the height of the transmitting and receiving antennas are $40\text{ m}$ and $25\text{ m}$, respectively. Also, determine the field strength at the receiving end.

The complete step-by-step mathematical solution to this numerical is detailed in [[5.07 Solved PYQ Numerical Bank - Waves & Propagation]].

---

9. Common Mistakes That Cost Marks

Avoid these exam pitfalls:

1. Confusing Reflection with Refraction: Never state that sky waves “reflect” off the ionosphere. The physical process is gradual refraction due to a decreasing refractive index gradient. Use the term refraction to secure full marks.
2. Neglecting Effective Earth Radius in LOS Calculations: Terrestrial calculations require the effective Earth radius $R^{\prime }=\frac{4}{3}R$ to account for tropospheric refraction. Do not use the geometric optical horizon factor ($3.57$) unless explicitly asked; always default to the radio horizon factor ($4.12$).
3. Incomplete Explanations for Ground Wave Limits: When explaining why ground waves fail above $2\text{ MHz}$, you must explain both mechanisms: (a) conduction losses in the soil increasing with frequency, and (b) the reduction in skin depth ($\delta \propto 1/\sqrt{f}$) confining currents to a thin surface layer and increasing resistive losses.
4. Unit Errors in electron density ($N$): In ionospheric calculations, electron density is often given as electrons per cubic centimeter (${\text{cm}}^{-3}$). You must convert this to electrons per cubic meter (${\text{m}}^{-3}$) by multiplying by $10^6$ before using the plasma frequency equation $f_p\approx 9\sqrt{N}$.
5. Forgetting TEM wave components: When defining a TEM wave, you must state that both $\vec{E}$ and $\vec{H}$ are transverse to the direction of propagation ($E_z=H_z=0$). Explaining only one component is incomplete.

---

10. PYQ Bank — Verbatim Questions & Answer Plans

Q1 — Propagation Modes & Service Selection [PYQ: 2015, 2019, 2021, 2022 — 10 Marks]

“State the mode of propagation for each of the following services and explain the reason: i) FM radio broadcasting, ii) SW radio-broadcasting, iii) Cellular telephones, iv) Satellite communication.”

Answer Plan: For each service, state the selected mode and the physical rationale:

• SW: Sky wave ($3\text{–}30\text{ MHz}$). Refraction in ionized layers allows intercontinental hops with low ground loss.
• FM: Space wave/LOS ($88\text{–}108\text{ MHz}$). VHF penetrates the ionosphere, high bandwidth, and immune to ionospheric fading.
• Cellular: Space wave ($700\text{ MHz}\text{–}3.5\text{ GHz}$). localised cells allow frequency reuse due to rapid horizon attenuation.
• Satellite: Space wave ($1\text{–}30\text{ GHz}$). Frequencies far above critical frequency pierce the ionosphere to reach orbit. (See §1 & §2 for detailed reasons).

Q2 — Types of Propagation & Examples [PYQ: 2017, 2018, 2023 — 12 Marks]

“What are the different types of propagation of radio waves from the radiating antenna to the receiving antenna? Explain with their practical examples.”

Answer Plan: Classify the three modes:

1. Ground Wave: Guided along Earth boundary, $<2\text{ MHz}$. Example: AM broadcasting, VLF submarine communication.
2. Sky Wave: Ionospheric refraction, $3\text{–}30\text{ MHz}$. Example: Shortwave broadcasting, HAM radio.
3. Space Wave: Direct Line-of-Sight, $>30\text{ MHz}$. Example: LTE/5G mobile, satellite links. (Provide the comparison matrix from §1 and draw the transmitter-receiver propagation path diagram).

Q3 — Ground Wave Limit & Earth Curvature [PYQ: 2016 — 08 Marks]

“Why ground wave propagation is not suitable for more than 2 MHz? Also explain the effects of earth’s curvature on radio wave propagation.”

Answer Plan:

• Part 1 ($>2\text{ MHz}$): Explain resistive soil losses scaling with frequency and skin depth reduction ($\delta =1/\sqrt{\pi f\mu \sigma }$), causing wave absorption.
• Part 2 (Curvature): Detail the radio horizon limit, diffraction at low frequencies (allowing waves to follow Earth’s profile), tropospheric refraction (bending waves down, modeled by $4/3R$), and shadow zones at high frequencies. (See §4 & §5 for complete text).

Q4 — Line of Sight (LOS) Distance Derivation [PYQ: 2016, 2019 — 11 Marks]

“Explain line of sight communication mode. Determine the maximum distance between two antennas in case of line of sight communication.”

Answer Plan:

• Define LOS communication (space waves travelling straight, blocked by horizon).
• Draw the geometry diagram showing antennas $h_t,h_r$, horizon distances $d_t,d_r$, and Earth radius $R$.
• Derive $d_t=\sqrt{2R{h}_t}$ and $d_r=\sqrt{2R{h}_r}$ using the Pythagorean theorem, showing the step where $h^2\ll 2Rh$ allows neglecting the height square.
• Explain tropospheric refraction and scale $R$ to $R^{\prime }=\frac{4}{3}R$ to obtain the radio horizon formula $d\approx 4.12(\sqrt{h_t}+\sqrt{h_r})$ km. (See §3 for complete math steps).

Q5 — Ionospheric Terms [PYQ: 2015, 2016, 2018 — 06 Marks]

“Define i) Virtual height, ii) skip distance, iii) maximum usable frequency (MUF)- as used in radio wave propagation.”

Answer Plan: State the clear definitions as written in §6. Write the formula for virtual height ($h^{\prime }=ct/2$) and the Secant Law formula for MUF.

Q6 — Virtual Height vs. Actual Height [PYQ: 2018, 2020, 2021 — 08 Marks]

“What is meant by virtual height in wave propagation? Why virtual height is used rather than actual height?”

Answer Plan:

• Define virtual height (§6.B).
• Explain why it is used: (1) Actual height is unmeasurable due to gradual refraction. (2) Wave slows down inside the layer (group velocity $<c$), making virtual height greater than actual height. (3) Virtual height forms a simplified straight-line triangle that yields the mathematically correct ground range and antenna angles.

Q7 — Standing Wave Creation on Conductor [PYQ: 2018 — 08 Marks]

“Why standing wave is created when a plane electromagnetic wave incident normally on a plane conducting boundary. Explain it with necessary equation.”

Answer Plan:

• Explain that when a wave is incident on a perfectly conducting boundary, it cannot penetrate it. To satisfy the boundary condition that the total tangential electric field must be zero at the surface, a reflected wave of equal amplitude but opposite phase ($\Gamma =-1$) is generated.
• Show mathematical equations:
  • Incident: $E_i(x,t)={\hat{a}}_y{E}_0\cos (\omega t-\beta x)$
  • Reflected: $E_r(x,t)=-{\hat{a}}_y{E}_0\cos (\omega t+\beta x)$
  • Total: $E_1(x,t)={\hat{a}}_{y}2E_0\sin (\beta x)\sin (\omega t)$
• Explain that this total field is a standing wave because the space dependency ($\sin \beta x$) and time dependency ($\sin \omega t$) are completely separated, meaning the wave amplitude oscillates in time but does not propagate spatially.

---

11. Self-Check Before Moving On

• Can you define Ground, Sky, and Space wave propagation, listing their frequency limits?
• Can you explain why ground wave propagation fails above $2\text{ MHz}$ using the skin depth formula?
• Can you state the selected propagation mode for SW, FM, Cellular, and Satellite services, and justify the choices?
• Can you derive the maximum Line-of-Sight distance formula $d\approx 3.57(\sqrt{h_t}+\sqrt{h_r})$ from basic geometry?
• Can you explain why the effective Earth radius coefficient $k=4/3$ is used to adjust the formula to $4.12$?
• Can you define Virtual Height, Skip Distance, Critical Frequency, MUF, and Minimum Usable Frequency?
• Can you explain why virtual height is used in propagation models rather than the actual refraction height?
• Can you write down the mathematical criteria ($E_z=H_z=0,\vec{E}\cdot \vec{H}=0$) and propagation direction vector equations for TEM waves?

---

Source: 05 electromagnetic_waves_master_notes.md §6 (master dump), ECE 2105 Syllabus Week 13, ECE 2105 field pyq.md, Masuk sir-2309008.pdf, Sadiku Ch. 10 & 15.